$$ \begin{aligned} 4z+14 &= 3z+13&& \text{move the $ \color{blue}{ 3z } $ to the left side and $ \color{blue}{ 14 }$ to the right} \\[1 em]4z-3z &= 13-14&& \text{simplify left and right hand side} \\[1 em]z &= -1&& \\[1 em]z &= -1&& \\[1 em] \end{aligned} $$